[Wisemanleo]

If I were to treat cook the reagents up under Grubbs conditions, any opinions on whether a metathesis would occur as I drew out below to form the product?

[kiwi]

nope, you wouldn't see metathesis. both olefins are too deactivated, especially the 1,1-disubsituted enone. i doubt they'd even ring close together, let alone cross. i've been stuck in a similar position, trying 5,8 membered ring closure, as well as cross. screened GI, GII, HGI, HGII, Grubbs bis(bromoPy) catalysts, screened solvents temperatures, reaction times - nothing worked. but swap one olefin for a terminal alkene - viola 92% yield of cross product first go. so you really have to pick your battles with metathesis.

[Wisemanleo]

Oh, that's good to know. I was about to buy the reagents, too. But why are they not activated enough?

[kiwi]

you've read the JACS paper on CM selectivity? CM is an equilibirium process (well of sorts), so in order to force some directionality (ie. drive reactants -> products), you need to introduce something to impede the further reactions of the CM product. typically this is done by setting it up like this:

very reactive olefin + poorly reactive olefin -> poorly reactive product

and most of the published examples follow this embodiment of that:

terminal mono-substituted olefin + acrylate ester -> a,b unsaturated ester

But you have two poorly reactive olefins - both with electron withdrawing groups, and one is 1,1 disubstituted as well. In my system, this combination of two deactivating effects turned my olefin into a spectator olefin.
As both olefins are of similar reactivity, you'll see a lot of equilibration (if you see anything at all).
Its probably still worth trying if you're keen - i'd be interested to see the result. Its definately going to be a challenging system imho though.
You might be able to get the same product by swapping the enone for the corresponding allylic alcohol, then oxidising the product. or alternatively, prepare the acrylate ester of the allylic alcohol, and then you are doing a  5-membered RCM as opposed to a CM. Transesterify, then oxidise. But at this stage, its starting to get a bit steppy.

[Wisemanleo]

I have not read that paper! That is probably why I didn't understand why the CM wouldn't work. I ran a quick search...I believe this is the article you are referring to?
J. Am. Chem. Soc., 125 (37), 11360 -11370

Anyways, you have brought up some excellent points! I'll be going back to the drawing board to figure out a different approach. I agree that it might actually be worth trying, so I might still cook this up small-scale and confirm what happens.

[kiwi]

Well with that paper in hand you'll see what i mean about olefin reactivity. It's worth giving a go when you sort out a good system - when it works it's like magic.